Chill a mixing bowl and beaters if possible. Whip the cold heavy cream with the confectioners’ sugar and vanilla until medium-stiff peaks form, taking care not to overwhip.

Spread a thin layer of whipped cream over the bottom of a 9-by-13-inch baking dish. Arrange a single layer of graham crackers over the cream, breaking pieces as needed to cover the dish.

Spread approximately one-quarter of the remaining whipped cream over the graham crackers. Add a layer of sliced strawberries and blueberries.

Repeat the graham-cracker, whipped-cream, and berry layers two more times. Finish the cake with the remaining whipped cream spread over the top.

Cover the dish tightly with plastic wrap and refrigerate for at least 4 hours. For the softest, cake-like texture, chill the dessert for 6–8 hours or overnight.

Decorate with fresh berries and optional graham-cracker crumbs immediately before serving. Slice with a sharp knife and serve cold.